The focus of this paper is to motivate and develop a Stein method for the manifold \(\mathbb {S}^1 = \lbrace x \in \mathbb {R}^2 : |x|^2=1\rbrace \) , and in particular, provide examples of bounds between popular distributions within directional statistics. We shall take a kernel based route similar to that of [1]} which avoids the need to directly bound the solution to the Stein equation. We shall motivate as to why below.
